We can correct the illusion by increasing the blue line’s length until the red line is equal to the actual distance
\[ \text{Lie Factor} = \frac{\text{Effect Size}_{graphic}}{\text{Effect Size}_{data}} \]
\[ \text{Lie Factor (Brain)} = \frac{\text{Effect Size}_{perception}}{\text{Effect Size}_{graphic}} \]
Hierarchical Bayesian model for \(\theta\), the overall lie factor
- Uniform priors on \(1\leq \mu\leq 4\), \(.1\leq\sigma\leq 2\)
- \(f(\theta | P, \mu, \sigma)\sim \text{Truncated Normal}(\mu, \sigma)\), \(\theta>1\)